[gf000]

So by this very definition it's mathematically wrong to have a single axis for all that.

Also, median person or position? The first is definable, the latter is hardly. There is no neutral/middle position in binary questions. What's a neutral position in abortion? Only allow half of them based on coin flips?

[simondotau]

Any problems are inherent in the left-right metaphor.

To speed-run your second paragraph: (1) Absolutely the median person for any given question. (2) Suggesting that there's anything "neutral" about a median position is to catastrophically mix metaphors. They aren't remotely synonymous. (3) The failure of a highly partisan person to acknowledge gradations doesn't mean they don't exist.